Bi-Lipschitz and differentiable sufficiency of weighted jets

João Carlos Ferreira Costa, Marcelo José Saia, and Carlos Humberto Soares Junior

Journal of Singularities
volume 25 (2022), 123-133

Received: 28 January 2021. Received in revised form: 3 September 2021.

DOI: 10.5427/jsing.2022.25f

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Abstract:

In this work we study bi-Lipschitz and differential sufficiency in the set of weighted jets of map germs of weighted degree. Our main result improves the degree of sufficiency of jets in the classical jet space obtained by Takens and by Martins-Fávaro. Moreover, we give a condition for the bi-Lipschitz sufficiency in both the weighted and non-weighted cases. Bi-Lipschitz sufficiency was not considered in those previously cited works.

2010 Mathematical Subject Classification:

58K15, 58K40, 58K65

Key words and phrases:

sufficiency of jets, weighted jets

Author(s) information:

João Carlos Ferreira Costa
Universidade Estadual Paulista (UNESP)
Instituto de Biociências, Letras e Ciências Exatas
Câmpus de São José do Rio Preto-SP, Brazil
joao.costa@unesp.br

Marcelo José Saia
Departamento de Matemática, CCET-UFSCar
Câmpus de São Carlos-SP, Brazil
mjsaia@ufscar.br

Carlos Humberto Soares Junior
Departamento de Matemática, CCN-UFPI
Câmpus Petrônio Portela, Teresina-PI, Brazil
humberto@ufpi.edu.br